Package dev.nm.stat.timeseries.linear.multivariate.stationaryprocess.arma

Class VARMAXModel

java.lang.Object

dev.nm.stat.timeseries.linear.multivariate.arima.VARIMAXModel

dev.nm.stat.timeseries.linear.multivariate.stationaryprocess.arma.VARMAXModel

Direct Known Subclasses:

VARXModel

public class VARMAXModel
extends VARIMAXModel

The VARMAX model (ARMA model with eXogenous inputs) is a generalization of the ARMA model by incorporating exogenous variables. X_t is an ARMAX(p, q) process, for which \[ X_t = \mu + \sum \phi_i X_{t-i} + \sum \theta_j \epsilon_{t-j} + \psi' D_t + \epsilon_t, \] X_t, μ and ε_t are n-dimensional vectors. The (n * n) matrices \({\phi_i}\) and \({\theta_j}\) are the AR and MA coefficients respectively. D_t is an (m * 1) vector which contains all exogenous variables at time t (excluding the intercept term), and its coefficients are represented by an (n * m) matrix ψ.

See Also:

Wikipedia: Autoregressive moving average model - Generalizations

Constructor Summary

Constructors

Constructor	Description
VARMAXModel(Matrix[] phi, Matrix[] theta, Matrix psi)	Construct a multivariate ARMAX model with unit variance and zero-intercept (mu).
VARMAXModel(Matrix[] phi, Matrix[] theta, Matrix psi, Matrix sigma)	Construct a multivariate ARMAX model with zero-intercept (mu).
VARMAXModel(Vector mu, Matrix[] phi, Matrix[] theta, Matrix psi)	Construct a multivariate ARMAX model with unit variance.
VARMAXModel(Vector mu, Matrix[] phi, Matrix[] theta, Matrix psi, Matrix sigma)	Construct a multivariate ARMAX model.
VARMAXModel(VARMAXModel that)	Copy constructor.
VARMAXModel(ARMAXModel model)	Construct a multivariate model from a univariate ARMAX model.

Method Summary

Modifier and Type	Method	Description
Matrix	armaxMean(Matrix arLags, Matrix maLags, Vector exVar)	Compute the multivariate ARMAX conditional mean.

Methods inherited from class dev.nm.stat.timeseries.linear.multivariate.arima.VARIMAXModel

AR, d, dimension, getVARMAX, MA, maxPQ, mu, p, phi, psi, q, sigma, theta

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

VARMAXModel

public VARMAXModel(Vector mu,
                   Matrix[] phi,
                   Matrix[] theta,
                   Matrix psi,
                   Matrix sigma)

Construct a multivariate ARMAX model.

Parameters:

mu - the intercept (constant) vector

phi - the AR coefficients (excluding the initial 1); null if no AR coefficient

theta - the MA coefficients (excluding the initial 1); null if no MA coefficient

psi - the coefficients of the deterministic terms (excluding the intercept term)

sigma - the white noise covariance matrix

VARMAXModel

public VARMAXModel(Vector mu,
                   Matrix[] phi,
                   Matrix[] theta,
                   Matrix psi)

Construct a multivariate ARMAX model with unit variance.

Parameters:

mu - the intercept (constant) vector

phi - the AR coefficients (excluding the initial 1); null if no AR coefficient

theta - the MA coefficients (excluding the initial 1); null if no MA coefficient

psi - the coefficients of the deterministic terms (excluding the intercept term)

VARMAXModel

public VARMAXModel(Matrix[] phi,
                   Matrix[] theta,
                   Matrix psi,
                   Matrix sigma)

Construct a multivariate ARMAX model with zero-intercept (mu).

Parameters:

phi - the AR coefficients (excluding the initial 1); null if no AR coefficient

theta - the MA coefficients (excluding the initial 1); null if no MA coefficient

psi - the coefficients of the deterministic terms (excluding the intercept term)

sigma - the white noise covariance matrix

VARMAXModel

public VARMAXModel(Matrix[] phi,
                   Matrix[] theta,
                   Matrix psi)

Construct a multivariate ARMAX model with unit variance and zero-intercept (mu).

Parameters:

phi - the AR coefficients (excluding the initial 1); null if no AR coefficient

theta - the MA coefficients (excluding the initial 1); null if no MA coefficient

psi - the coefficients of the deterministic terms (excluding the intercept term)

VARMAXModel

public VARMAXModel(ARMAXModel model)

Construct a multivariate model from a univariate ARMAX model.

Parameters:

model - a univariate ARIMA model

VARMAXModel

public VARMAXModel(VARMAXModel that)

Copy constructor.

Parameters:

that - a multivariate ARMAX model

Method Detail

armaxMean

public Matrix armaxMean(Matrix arLags,
                        Matrix maLags,
                        Vector exVar)

Compute the multivariate ARMAX conditional mean.

Parameters:

arLags - the AR lags

maLags - the MA lags

exVar - the exogenous variables

Returns:

the conditional mean